### Archives

### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Generalizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014

### Keywords

L-space Weakly compact cardinal Mandelbrot set 05A17 Shelah's Strong Hypothesis Microscopic Approach Martin's Axiom P-Ideal Dichotomy weak square sap Chromatic number incompactness diamond star b-scale Coherent tree Uniformization Souslin Tree 20M14 Cohen real Knaster Singular coﬁnality Prevalent singular cardinals polarized partition relation square principles Cardinal Invariants Club Guessing Fat stationary set Slim tree Erdos-Hajnal graphs Small forcing Nonspecial tree Square-Brackets Partition Relations S-Space stationary reflection free Boolean algebra PFA(S)[S] Constructible Universe Almost Souslin 11P99 Rado's conjecture Hindman's Theorem Forcing tensor product graph Minimal Walks Fodor-type reflection Commutative cancellative semigroups Distributive tree Prikry-type forcing Sakurai's Bell inequality Hereditarily Lindelöf space very good scale Successor of Singular Cardinal Stevo Todorcevic weak diamond Large Cardinals Luzin set PFA middle diamond super-Souslin tree Selective Ultrafilter Universal Sequences Axiom R Diamond coloring number Rock n' Roll Poset Kurepa Hypothesis stationary hitting Reduced Power Chang's conjecture HOD Generalized Clubs Postprocessing function Dushnik-Miller Aronszajn tree Jonsson cardinal Erdos Cardinal Antichain Rainbow sets Cardinal function Almost-disjoint famiy Uniformly coherent projective Boolean algebra Singular Density square Ascent Path Singular cardinals combinatorics Absoluteness reflection principles Foundations Whitehead Problem Parameterized proxy principle Fast club Successor of Regular Cardinal xbox Ostaszewski square Forcing Axioms Hedetniemi's conjecture OCA approachability ideal Non-saturation ccc Almost countably chromatic Partition Relations

# Tag Archives: Singular Density

## On topological spaces of singular density and minimal weight

Abstract: We introduce a weakening of the Generalized Continuum Hypothesis, which we will refer to as the Prevalent Singular cardinals Hypothesis (PSH), and show it implies that every topological space of density and weight $\aleph_{\omega_1}$ is not hereditarily Lindelöf. The assumption … Continue reading

## Workshop on Set Theory and its Applications, February 2007

These are the slides of a talk given at the Workshop on Set Theory and its Applications workshop (Weizmann Institute, February 19, 2007). Talk Title: Nets of spaces having singular density Abstract: The weight of a topological space X is the … Continue reading

## On the consistency strength of the Milner-Sauer conjecture

Abstract: In their paper from 1981, Milner and Sauer conjectured that for any poset $\mathbb P$, if $\text{cf}(\mathbb P)$ is a singular cardinal $\lambda$, then $\mathbb P$ must contain an antichain of size $\text{cf}(\lambda)$. The conjecture is consistent and known … Continue reading